On the structure of Ammann A2 tilings
Logic
2018-02-21 v5
Abstract
We establish a structure theorem for the family of Ammann A2 tilings of the plane. Using that theorem we show that every Ammann A2 tiling is self-similar in the sense of [B. Solomyak, Nonperiodicity implies unique composition for self-similar translationally finite tilings, Discrete and Computational Geometry 20 (1998) 265-279]. By the same techniques we show that Ammann A2 tilings are not robust in the sense of [B. Durand, A. Romashchenko, A. Shen. Fixed-point tile sets and their applications, Journal of Computer and System Sciences, 78:3 (2012) 731--764].
Cite
@article{arxiv.1112.2896,
title = {On the structure of Ammann A2 tilings},
author = {Bruno Durand and Alexander Shen and Nikolay Vereshchagin},
journal= {arXiv preprint arXiv:1112.2896},
year = {2018}
}